The sum of two angles is $89^\circ$. Angle 2 is $161^\circ$ smaller than $4$ times angle 1. What are the measures of the two angles in degrees?
Answer: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 89}$ ${y = 4x-161}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${4x-161}$ for $y$ in the first equation. ${x + }{(4x-161)}{= 89}$ Simplify and solve for $x$ $ x+4x - 161 = 89 $ $ 5x-161 = 89 $ $ 5x = 250 $ $ x = \dfrac{250}{5} $ ${x = 50}$ Now that you know ${x = 50}$ , plug it back into $ {y = 4x-161}$ to find $y$ ${y = 4}{(50)}{ - 161}$ $y = 200 - 161$ ${y = 39}$ You can also plug ${x = 50}$ into $ {x+y = 89}$ and get the same answer for $y$ ${(50)}{ + y = 89}$ ${y = 39}$ The measure of angle 1 is $50^\circ$ and the measure of angle 2 is $39^\circ$.